Friction is often the trickiest part of Newton's Laws problems. Understanding its behavior is crucial.

Static vs Kinetic:

• Static friction acts when surfaces are at rest relative to each other
• It is self-adjusting: $f_s$ = applied force (up to $mu_s$*N)
• At the verge of motion, $f_s$ = $mu_s$*N (maximum)
• Once motion begins, friction drops to $f_k$ = $mu_k$*N
• $mu_k$ < $mu_s$ always

Direction of Friction:

• Opposes RELATIVE motion (kinetic) or TENDENCY of relative motion (static)
• Friction on a walking person's foot is FORWARD
• Friction on a box in an accelerating truck is FORWARD
• Friction is not always opposite to the direction of motion

Angle of Repose:

• The maximum angle at which a block remains stationary on a rough incline
• tan(alpha) = $mu_s$
• For theta > alpha: block slides
• For theta < alpha: block is stationary with f = mg*sin(theta) < $mu_s$*N
• For theta = alpha: block is on the verge of sliding

Optimal Pulling Angle:

• To move a block on a rough surface with minimum force, pull at angle lambda = arctan($mu_s$) above horizontal
• This minimizes the normal force and therefore friction
• $F_{min}$ = mg*$mu_s$/sqrt(1 + $mu_s^2$)